CN105262494A - Polar code BP decoding method with iterative early-stopping mechanism - Google Patents

Abstract

The invention discloses a polar code BP decoding method with an iterative early-stopping mechanism. The polar code BP decoding method belongs to the field of channel coding technology. According to the polar code BP decoding method, a BP decoding algorithm is used for decoding the polar coding information. The polar coding information is obtained through performing CRC coding and polar coding on original information. In each iteration process for decoding the polar coding information by means of the BP decoding algorithm, CRC verification is performed on the decoding result which is obtained through current iteration process. If verification is passed, iteration is stopped and the decoding result which is obtained through current iteration process is output; and otherwise, iteration is performed continuously until a preset maximal number of iterations is reached. Compared with the prior art, the polar code BP decoding method has advantages of effectively reducing computing difficulty and decoding time delay in decoding and furthermore facilitating hardware realization.

Description

A kind of have the polarization code BP interpretation method that iteration early stops mechanism

Technical field

The present invention relates to a kind of polarization code interpretation method, particularly relate to a kind of polarization code BP interpretation method with iteration early stopping mechanism, belong to channel coding technology field.

Background technology

Polarization code (polarcode) is proposed in " ChannelPolarization:AMethodforConstructingCapacity-Achie vingCodesforSymmetricBinary-InputMemorylessChannels " literary composition by ErdalArikan.He from theoretic demonstrate through channel combination be separated, when channel quantity is tending towards infinity, a part of channel is tending towards perfect, and a part of channel is tending towards pure noisy communication channel, is called channel-polarization phenomenon.We choose reasonable channel in aggregate channel based on this channel-polarization phenomenon, structure polarization code.ErdalArikan demonstrates when channel quantity is tending towards infinite, and polarization code can be tending towards shannon limit in theory.

The main interpretation method of polarization code has SC decoding [E.Arikan, " Channelpolarization:Amethodforconstructingcapacityachiev ingcodesforsymmetricbinary-inputmemorylesschannels; " InformationTheory, IEEETransactionson, vol.55, no.7, pp.3051 – 3073,2009.] and BP decoding [E.Arikan, " Aperformancecomparisonofpolarcodesandreed-mullercodes, "

CommunicationsLetters,IEEE,vol.12,no.6,pp.447–449,2008.]。SC decoding computation complexity is low, and has good error-correcting performance, but due to the serial arithmetic structure of SC algorithm inherence, it exists long decoding latency.To be ErdalArikan propose in literary composition at " APerformanceComparisonofPolarCodesandReed-MullerCodes " in BP decoding.He demonstrates because polarization code can represent with factor graph, so polarization code can use the method decoding of BP (belief propagation).Compare with SC decoding, BP decoding is due to its inherent parallel organization, and decoding latency is much smaller than SC decoding.But just can obtain reliable decode results because BP decoding needs to carry out successive ignition, the computation complexity of BP decoding is very high.In order to the decoding complexity of less BP decoding, early stop (or claiming premature termination) algorithm very important.Early stop algorithm referring to detecting adaptively in decoding iteration process whether to obtain reliable decoding to export, if condition meets can terminate decoding at once.Early stop algorithm can reducing decoding complexity and decoding delay linearly.

Iteration early stops the core of mechanism to be how to judge that the decoding that current iteration walks exports enough reliable.Existing researcher proposes and has the polarization code BP interpretation method that iteration early stops mechanism at present, such as, (publication number is CN104539296A to one section of Chinese patent, publication date is 2015-4-22) disclose " a kind of polarization code based on premature termination iterative strategy improves BP interpretation method ", the method utilizes the average of the double variable quantity of the left information value of the likelihood ratio of the information bit of polarization code to be less than the judgment criterion of a predetermined threshold value as iteration premature termination, to reduce decoding complexity and the decoding delay of BP polarization interpretation method.But the method can not prove that the iterations needed for it is minimum, although decrease iterations to a certain extent, iterations still exists redundancy.The method needs to utilize the likelihood ratio numerical information of continuous three iteration to calculate simultaneously, and computation complexity is higher, and hardware (register) expends greatly.Final step due to BP decoding be by the symbol of the left information of the likelihood ratio of information bit nonumeric carry out adjudicating translate information bit, and numerical value change is less than a predetermined threshold value as iteration premature termination condition by this patent, is not obviously optimum.And predetermined threshold value is a certain fixed value, can not be suitable for the situation that in realistic communication scene, channel conditions is complicated and changeable, not have adaptivity.

Summary of the invention

Technical problem to be solved by this invention is to overcome prior art deficiency, provides a kind of and has the polarization code BP interpretation method that iteration early stops mechanism, effectively can reduce computation complexity and the decoding delay of decoding, be convenient to hardware implementing simultaneously.

The present invention is concrete by the following technical solutions:

There is the polarization code BP interpretation method that iteration early stops mechanism, utilize BP decoding algorithm to carry out decoding to Polarization Coding information; Described Polarization Coding information obtains by carrying out Polarization Coding again after first carrying out CRC coding to raw information; Carry out in the iterative process each time of decoding utilizing BP decoding algorithm to Polarization Coding information, all the decode results obtained is walked to current iteration and carry out CRC check, as passed through verification, then stop iteration and export current iteration walking the decode results obtained, otherwise, proceed iteration, until reach default maximum iteration time.

Compared to existing technology, the inventive method significantly can reduce decoding iteration number of times when not causing decoding performance to lose, and especially in high s/n ratio channel, effect is more obvious.And the method reliability is high, highly sensitive, and hardware implementing is simple.In addition, due to the loss that CRC is enough little, the decoding iteration number of times of interpretation method of the present invention can regard fully necessary as, namely can regard that decoding obtains that reliable decoding exports as minimum iterations.Therefore, the present invention also can as the criterion of each BP algorithmic statement speed of a kind of constant.

Accompanying drawing explanation

The factor graph of Fig. 1 to be code length be polarization code of 8;

Fig. 2 is the elementary cell of polarization code factor graph;

Fig. 3 is the schematic flow sheet of the inventive method;

Fig. 4 is the Performance comparision of the inventive method and conventional polar code BP interpretation method;

Fig. 5 is the mean iterative number of time of the inventive method in different signal to noise ratio channel.

Embodiment

Below in conjunction with accompanying drawing, technical scheme of the present invention is described in detail:

The BP decoding algorithm of traditional polarization code is the information transmitting log-likelihood ratio on the such as factor graph shown in Fig. 1 (polarization code being 8 for code length) successively to the right left.Fig. 2 shows the elementary cell of polarization code factor graph.One row bit corresponding informance u of factor graph high order end, the corresponding code word x of a row bit of low order end.(i, j) represents from i-th arranging from left to right, the node of jth row.Each node has two amount of information, and the amount of information passing through node (i, j) is from right to left designated as L by us _i,j, the amount of information from left to right passing through node (i, j) is designated as R _i,j, these information are that form transmits renewal mutually with LLR.In decode procedure, first according to the following formula initialization is carried out to the R information of high order end and the L information of low order end:

$R_{1,j}=\left\{\begin{array}{ccc}0,& if& j\∈A\\ \mathrm{\∞},& if& j\∉A\end{array}\right.---\left(1\right)$

$L_{n+1,j}=ln\left(\frac{P\left(y_j\right|x_j=0)}{P\left(y_j\right|x_j=1)}\right)---\left(2\right)$

A in formula refers to the set of information bit.Then log-likelihood ratio information is upgraded according to following formula respectively to the left transmission of dextrad:

L _i，j＝g(L _i+1，2j-1，L _i+1，2j+R _i，j+N/2)

L _i，j+N/2＝g(R _i，j，L _i+1，2j-1)+L _i+1，2j

(3)

R _i+1，2j-1＝g(R _i，j，L _i+1，2j+R _i，j+N/2)

R _i+1，2j＝g(R _i，j，L _i+1，2j-1)+R _i，j+N/2

g(x，y)≈0.9·sign(x)sign(y)min(|x|，|y|)

After reaching default maximum iteration time, be then decoded as 0 in this position if not information bit, otherwise according to high order end log-likelihood ratio L (1, the j) symbol of (1 represents first stage, i.e. high order end, and j represents jth position)

Judge that information bit is 0 or 1, judge that the formula of institute's foundation is as follows:

${\hat{u}}_j=\left\{\begin{array}{ccc}0,& if& L_{1,j}\&GreaterEqual;0\\ 1,& if& L_{1,j}<0\end{array}\right.---\left(4\right)$

The more detailed information of BP decoding algorithm about conventional polar code can list of references [E.Arikan, " Aperformancecomparisonofpolarcodesandreed-mullercodes, "

CommunicationsLetters,IEEE,vol.12,no.6,pp.447–449,2008.]。

In order to reduce computation complexity and the decoding delay of decoding, be convenient to hardware implementing simultaneously, thinking of the present invention utilizes cyclic redundancy check (CRC) (CyclicRedundancyCheck is called for short CRC) as judging in BP decode procedure that whether the decoding that current iteration walks exported foundation enough reliably.

CRC check is a kind of transfer of data error detection function, and it carries out polynomial computation to data, and is attached to after frame by the result obtained, and receiving equipment also performs similar algorithm, to ensure correctness and the integrality of transfer of data.When the loss of cyclic redundancy check (CRC) is enough low, the decoding meeting cyclic redundancy check (CRC) condition exports and is considered to reliable.As a kind of verification mode of maturation, CRC check have simple and convenient, be easy to hard-wired feature.

Specifically, the present invention carries out Polarization Coding again after coding side first carries out CRC coding to raw information; At decoding end, in each iteration of decoding, all judge whether the decode results obtained meets the condition of cyclic redundancy check (CRC), if met, stop iteration in advance, obtain decoding and export.

Consider that code length is the polarization code of N, wherein information bit has K position, at coding side, first sort according to the height of channel capacity, select the individual best channel of K, corresponding K position is information bit (informationbit), and remaining N-K position for freezing position (frozenbit), and will be freezed position and is all set to 0; Choose cyclic redundancy check (CRC) (R position) and the generator polynomial G (x) of appropriate length, with code length for 1024, information bit be 512 polarization code be example, adopt the performance of CRC-16 enough good, but decoding performance can be caused using CRC-8 to decline as stop condition morning; Then carry out CRC coding, by K-R position before K information bit as real information bit, then R position is as CRC check position, and x is multiplied by front K-R position ^rthe remainder obtained divided by generator polynomial G (x) is again exactly check code; The position of freezing of N-K position is fixed as 0, and K position information bit together constitutes wherein G is generator matrix, and will propagate in the channel.

If the code word that decoding end receives is first initialization is carried out according to formula (1), (2) information to the information of high order end and low order end; According to formula (3) lastest imformation, and check that decoding obtains whether meet CRC condition, if satisfied condition, consider that the CRC loss of selection is enough low, it is exactly that reliable decoding exports that decoding now exports, if do not satisfied condition, judges whether to reach maximum decoding number of times, if no, then continue lastest imformation, carry out next iteration.The basic procedure of the inventive method as shown in Figure 3.

Fig. 4 shows the inventive method and the special simulation result of the Montero of conventional polar code BP interpretation method in Gauss's additive white noise channel, and maximum iteration time is all set to 30 times.Polarization code code length is 1024, information bit 512, and the generator polynomial chosen is CRC-16.In figure, abscissa EbN0 is signal to noise ratio, ordinate errorrates is the error rate, and in legend, ber is bit error rate, and fer is frame error rate, constantiterations represents that iterations is constant, and CRC-16aided represents the BP interpretation method employing the present invention and propose.Can find out that the present invention when iterations is less than traditional BP decoding, can reach the decoding performance the same with traditional BP decoding according to Fig. 4.

Fig. 5 shows the mean iterative number of time of BP interpretation method of the present invention in different signal to noise ratio channel, and wherein CRC is respectively 32 and 16, and polarization code code length and information digit are 1024 and 512.In figure, EbN0 is signal to noise ratio, and avg_Iterations represents mean iterative number of time.Easily find out, the present invention can effectively reduce iterations, and especially in middle and high signal to noise ratio channel, effect is more remarkable.

Claims (1)

1. there is the polarization code BP interpretation method that iteration early stops mechanism, utilize BP decoding algorithm to carry out decoding to Polarization Coding information; It is characterized in that, described Polarization Coding information obtains by carrying out Polarization Coding again after first carrying out CRC coding to raw information; Carry out in the iterative process each time of decoding utilizing BP decoding algorithm to Polarization Coding information, all the decode results obtained is walked to current iteration and carry out CRC check, as passed through verification, then stop iteration and export current iteration walking the decode results obtained, otherwise, proceed iteration, until reach default maximum iteration time.